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Monitorability for the Hennessy–Milner logic with recursion

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Abstract

We study \(\mu \) HML, a branching-time logic with least and greatest fixpoints, from a runtime verification perspective. The logic may be used to specify properties of programs whose behaviour may be expressed as a labelled transition system. We establish which subset of this logic can be monitored for at runtime by merely observing the runtime execution of a program. A monitor-synthesis algorithm is defined for this subset, where it is shown that the resulting synthesised monitors correctly perform the required analysis from the observed behaviour. We also prove completeness results wrt. this logical subset that show that, up to logical equivalence, no other properties apart from those identified can be monitored for and verified at runtime.

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Notes

  1. These are normally expressed as structural equivalence rules such as \(p\!\parallel \!\textsf {nil} \equiv p\) and \(p\!\parallel \!q \equiv q\!\parallel \!p\) in standard CCS. We elide them here to alleviate our exposition.

  2. A transition sequence is maximal if it is either infinite or affords no more actions.

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Authors and Affiliations

  1. Department of Computer Science, ICT, University of Malta, Msida, Malta

    Adrian Francalanza

  2. School of Computer Science, Reykjavik University, Reykjavik, Iceland

    Luca Aceto & Anna Ingolfsdottir

Authors
  1. Adrian Francalanza
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  2. Luca Aceto
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  3. Anna Ingolfsdottir
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Corresponding author

Correspondence to Adrian Francalanza.

Additional information

The research of L. Aceto and A. Ingolfsdottir was partly supported by the Project 001-ABEL-CM-2013 of the NILS Science and Sustainability Programme. The research of all three authors was also supported by the project Theoretical Foundations of Monitorability (No. 163406-051) of the Icelandic Research Fund.

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Francalanza, A., Aceto, L. & Ingolfsdottir, A. Monitorability for the Hennessy–Milner logic with recursion. Form Methods Syst Des 51, 87–116 (2017). https://doi.org/10.1007/s10703-017-0273-z

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